Ancient Babylonians employed geometry and an early form of calculus to predict the path of Jupiter

Living in present-day Syria and Iraq between 18th century and 6th century BC, the ancient Babylonians were quite advanced when it came to astronomy, using simple arithmetic to estimate the position of different celestial bodies, including the sun, the moon and the various planets. According to a new research, however, they were also responsible for making great strides in mathematics, particularly geometry and calculus. They employed sophisticated geometrical techniques to predict the movements of Jupiter, some 1,400 years before such methods were invented in medieval Europe.

As the researchers point out, the techniques used by the ancient Babylonians eventually paved the way for the development of calculus, a branch of mathematics that deals with change measured over time. The study, recently published in the Science journal, was conducted by an international team of researchers. Although the knowledge of algebra and geometry were easily available during ancient times, both in Babylonia and ancient Greece, the current evidence indicates, possibly for the first time, that the Babylonian astronomers knew how to use geometry to track the movements of planets. Speaking about the find, Mathieu Ossendrijer, a professor at Berlin’s Humboldt University and the study’s author, said:

What is new is that the Babylonians also used geometry in their astronomy. We have evidence that they used geometrical figures to gauge the motion of planets but the really exciting thing is that the kind of geometry they used is very special. What we have found essentially is almost like a modern-day graph – a geometrical figure that represents an abstract mathematical space. That’s really new and exciting as it was thought to have been first invented much later, around 1350.

For the research, the team studied clay tablets, dating back to period between 350 BC and 50 BC. Currently kept in London’s British Museum, the tablets contain Babylonian cuneiform text, likely etched by scholars and priests living during that time. Analysis of the text has revealed that these ancient astronomers were computing the irregular motions of Jupiter over the course of 60 days, starting from a day when the planet first appeared above the horizon. For the Babylonians, the colossal planet represented their chief god, Marduk or the patron deity of the city of Babylon. Ossendrijer added:

The tablets were written by priests in the temple. They computed the position of all five planets that they knew about, but Jupiter had the largest number of texts devoted to it… It’s like a precursor if you like of what we know today as integral calculus, which allows us to calculate the movements of decelerating or accelerating objects. It’s a concept that was invented twice; once in ancient Babylonia and then re-invented around 1350 in medieval Europe. The ancient Greeks never did this.

When observed in the night sky, Jupiter’s movements appear to be quite slow, which in turn refers to the relative motion of its orbit with respect to that of Earth’s. Thus, a graph showing Jupiter’s relative velocity against time would form a trapezoid, with downward sloping sides. The trapezoid’s area would therefore provide the total distance covered by the planet during the 60-day period. According to the team, several of the tablets had trapezoidal figures carved on them, with the Babylonian scholars referring to the shape as the “oxen head”. Hermann Hunger, a professor at the University of Vienna and a member on the research team, said:

These findings do not so much show a higher degree of sophistication in geometric thinking, but rather a remarkable ability to apply traditional Babylonian geometric thinking to a new problem.